Addison put a $2290 item on layaway by making a 20% down payment and
1 answer:
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Answer:
a) Atleast 75%
b) Atleast 88.9%
c) 95%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 6.7
Standard Deviation, σ = 1.6
Chebyshev's Theorem:
- Atleast
percent of data lies within k standard deviation of mean.
Empirical Rule:
- Almost all the data lies within 3 standard deviation for a normal data.
- Around 68% of data lies within 1 standard deviation of mean.
- Around 95% of data lies within 2 standard deviation of mean.
- Around 99.7% of data lies within 3 standard deviations o mean.
a) minimum percentage of individuals who sleep between 3.5 and 9.9 hours
We have to find the percent of data lying within 2 standard deviation of mean.
Putting k = 2
Atleast 75% of of individuals who sleep between 3.5 and 9.9 hours.
b) minimum percentage of individuals who sleep between 2.7 and 10.7 hours
We have to find the percent of data lying within 3 standard deviation of mean.
Putting k = 3
Atleast 88.9% of of individuals who sleep between 2.7 and 10.7 hours.
c) percentage of individuals who sleep between 3.5 and 9.9 hours per day.
Thus, we have to find the percentage of data lying within 2 standard deviation.
By empirical rule, around 95% of data lies within 2 standard deviation.
Thus, 95% of of individuals who sleep between 3.5 and 9.9 hours.
This is higher than the percentage obtained from Chebyshev's rule.
Answer:
Account B earns more interest.
After 20 years, account B will have earned $171.89 more.
Step-by-step explanation:
Let's calculate the total for each account.
Account A:
Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:
Where A is the future value, P is the principal, r is the rate, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:
Multiply and add:
Multiply. So, the total amount of money in Account A after 20 years is:
Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of
Account B:
Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:
Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:
Simplify this to acquire:
Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:
Since our principal was $2000, this means that we earned an interest of approximately .
So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.
So, Account B earned more interest.
And it earned more than Account A.
And we're done!